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Journal of Applied Mathematics
Volume 2012, Article ID 257140, 10 pages
http://dx.doi.org/10.1155/2012/257140
Research Article

The Global Existence of Nonlinear Evolutionary Equation with Small Delay

School of Science, Tianjin Polytechnic University, Tianjin 300387, China

Received 11 April 2012; Accepted 9 May 2012

Academic Editor: Yonghong Yao

Copyright © 2012 Xunwu Yin. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We investigate the global existence of the delayed nonlinear evolutionary equation tu+Au=f(u(t),u(tτ)). Our work space is the fractional powers space Xα. Under the fundamental theorem on sectorial operators, we make use of the fixed-point principle to prove the local existence and uniqueness theorem. Then, the global existence is obtained by Gronwall’s inequality.